The Colombia goalkeeper could have a medical with the Gunners in the next 72 hours and link up with the club on its preseason tour of the USA.
The Gunners have agreed to a fee with Nice for Ospina and have discussed personal terms with the player as well as his role at Emirates Stadium next season.
Arsenal is hopeful Ospina will have a medical with the club in the next 72 hours and link up with the squad on its forthcoming tour of the United States.
The Londoners are confident that the keeper, who impressed at the World Cup, will become their third senior signing of the summer following the arrivals of Alexis Sanchez and Mathieu Debuchy.
Arsenal has opened talks with Southampton over a 15 million-pound move for midfielder Morgan Schneiderlin, although Tottenham is currently the favorite to sign the France international.
The Gunners have also held extensive discussions with Atletico Madrid about signing Javier Manquillo on a season-long loan, but the deal for the Spanish right back is currently on the backburner and the club is ready to pursue alternatives.
With a second right back set to sign for Arsenal, Carl Jenkinson is expected to be sent out on loan to West Ham for the forthcoming season in order to play regular first-team minutes.
The expected signing of another senior international keeper will also provide strong competition for Wojciech Szczesny, who was the No. 1 choice in both the Premier League and Champions League last season but was overlooked for the club's successful FA Cup campaign.
Wenger moved for Ospina after Arsenal failed to agree to a fee for David Marshall during talks with Cardiff City.
Ospina, 25, is regarded as good value given his experience and the Gunners were able to negotiate a lower fee as he only has a year remaining on his Nice contract.